Grade 9

SCHOOL GRADE LEVEL

DAILY LESSON LOG
LEARNING Mathematics
TEACHER
AREA
TEACHING Quarter 3
DATE AND QUARTER
TIME
I. OBJECTIVES • Define Pythagorean Theorem
• Demonstrate the relationship between the sum of the squares of the legs and the
square of the hypotenuse in Pythagorean theorem to derive its algebraic
representation.
• Prove Pythagorean Theorem
• Show appreciation of the application of the Pythagorean Theorem in real life.
A. Content Standards The learner demonstrates understanding of the key concepts of parallelograms and triangle
similarity.
B. Performance Standards The learner is able to investigate, analyze and solve problems involving parallelograms and
triangle similarity through appropriate and accurate representation.
C. Learning Competencies / The learner proves Pythagorean Theorem. (M9GE-IIIi-2)
Objectives
II. CONTENT Geometry
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pages Teacher’s Guide (TG) in Mathematics 9 pp.356-375
2. Learner’s Materials pages Learner’s Guide (LG) in Mathematics 9 pp.389-392
3. Textbook pages APEX Math Similarity of Triangles Unit 4 Lesson 11-16 Geometry Chapter 5 Similarity 5.4.2.
The Pythagorean Theorem p.16
Mathematics 9 by Orlando A. Oronce and Marilyn O. Mendoza pp. 348-352
4. Additional Materials PT Model – The Pythagorean Theorem Stand Model
Worksheets
B. Other Learning Resources Video lectures on the proof of Pythagorean Theorem https://youtu.be/BNCj-K2hd_k
Introduction to Pythagorean Theorem
https://mathbitsnotebook.com/Geometry/RightTriangles/RTpythagorean.html
Ways to prove the Pythagorean Theorem https://www.youtube.com/watch?v=YompsDlEdtc
Application of Pythagorean Theorem in Real-Life Situation
https://mathbitsnotebook.com/Geometry/RightTriangles/RTPythP ractice.html
IV. PROCEDURES
A. Reviewing the previous Review of the Lesson
lesson or presenting the new The students will be given a pair of questions with an illustration which they are to
lesson (ELICIT) reflect upon.

In ∆𝐴𝐵𝐶 at the right, A is a right angle, ̅̅̅̅

𝐴𝐷 is
the altitude to ̅̅̅̅
𝐵𝐶 .
1. Name the similar triangles
2. Find the values of x, y and z.

Students will be given time to reflect and answer the given questions. Afterwards, the
teacher will ask volunteers to present or give the answers. Subsequent to the sharing
of the answers, the teacher will then reinforce the recalling of the concepts regarding
Right Triangle Similarity before going further to the new lesson.

Presenting the new lesson.

Guess what it meant!
The teacher will flash several pictures and students will identify what word or phrase
the pictures are trying to convey.

1.
+ + +
2.

+ + + +
 3.
+

4.
+ +

5.
+
The teacher will now clarify that the words that were correctly identified have
something to with the lesson to be discussed. Guesses or any ideas will be
accommodated before the teacher formally introduces the new topic/discussion.
Then, students will be connected to it through the teacher presenting the objectives.

B. Establishing a purpose for a. Define Pythagorean Theorem

the lesson (ENGAGE) b. Demonstrate the relationship between the sum of the squares of the legs and the
square of the hypotenuse in Pythagorean theorem to derive its algebraic
representation.
c. Prove Pythagorean Theorem
C. Presenting examples/ Given the selection below, students will be asked to read, reflect and share their ideas and
instances of the new lesson answers regarding the questions at the end of the selection.
(ENGAGE)
Mode of Transportation During the New Normal

Subsequent to the outburst of the Covid-19 Pandemic, the “new normal” demands
social distancing – but with the state of the public transport systems, there is no way to avoid
a crowded commute. That’s why biking became championed as an ideal alternative: efficient,
affordable, and sustainable mode of transportation. With or without pandemic, biking is
beneficial– including lessening the volume of cars on the road, lowering pollution rate emitted
in air and the like.
Suppose that Mario, a resident of the nearby barangay,
planned to buy bread at a bakeshop. He usually rides his bike along
Simoun St. then up Casañas St. He knows that the two streets are
perpendicular and are 3 and 4 km long, respectively. An alternative
route is the Blumentritt Road as shown in the map at the right. Is
Blumentritt Road shorter? Which way saves more time?

Students’ responses will now be accommodated by the teacher, whether it be a logical,

systematic or the ideal one. Then, the teacher will then lead the discussion to what
Pythagorean Theorem is – the ideal way of solving and dealing with the questions in the
selection.

D. Discussing new concepts After the discussion of the definition of Pythagorean Theorem (not including its formula or
and practicing new skills #1 algebraic representation), using the PT model, students will be tasked to do a simple
(EXPLORE) investigation. The end goal is to observe and demonstrate the relationship between the
triangle and the squares with the same dimension as the side where these squares are built
upon. Students will list all their observations through the guide questions provided.
1. What kind of triangle is the figure at the center?
2. What features do the joined figures have in terms of their length, width, area, etc.?
3. What can you conclude about the geometric relationships of these figures?
4. If you were to create an equation and represent the joined figures algebraically,
what would it be?

After the students’ investigation, they will present their observations and findings. Then, the
teacher will supplement their prior understanding through showing the systematic proof of the
Pythagorean Theorem and introducing or confirming the correct algebraic representation of
it. They will then go back to the selection that has been provided and confirm the right answer
through applying the concept of Pythagorean Theorem.
E. Discuss new concepts and The teacher will provide examples and show a systematics way of finding the length of a side
practicing new skills #2 of a right triangle Using Pythagorean Theorem.
(EXPLORE)
 Example 1. (Solving for the length of the hypotenuse) Use the
Pythagorean Theorem to determine the value of 𝑥 in the figure at
the right.

Step 1. Identify the legs and the hypotenuse of the right triangle.
The legs have lengths 6 cm and 8 cm and 𝑥 is the length
of the hypotenuse, the side opposite the right angle.

Step 2. Substitute the variables by the given values into the

formula (remember ‘c’ is the length of the hypotenuse).
𝑎2 + 𝑏2 = 𝑐 2
62 + 82 = 𝑥 2

Step 3. Solve for the unknown.

62 + 82 = 𝑥 2
36 + 64 = 𝑥 2
100 = 𝑥 2
√100 = 𝑥
10 𝑐𝑚 = 𝑥

Therefore, the length of the hypotenuse of the right triangle is 10 cm.

Example 2. (Solving for length of the leg) Use the Pythagorean Theorem to determine the
value of x in the figure at the right.

Step 1. Identify the legs and the hypotenuse of the right

triangle. The legs have lengths 24 and x. The length of the
hypotenuse is 26.

Step 2. Substitute the variables by the given values into the

formula (remember ‘c’ is the length of the hypotenuse)
𝑎2 + 𝑏2 = 𝑐 2
𝑥 2 + 242 = 262

Step 3. Solve for the unknown.

𝑥 2 + 242 = 262
𝑥 2 + 576 = 676
𝑥 2 = 676 − 576
𝑥 2 = 676 − 576
𝑥 2 = 100
𝑥 = √100
𝑥 = 10

Therefore, the length of the other leg of the right triangle is 10 cm

F. Developing mastery Activity (10 mins.)
(EXPLAIN) Students will be given an activity sheet individually wherein they will apply what they
have learned about Pythagorean theorem to find the unknown side of the given right
triangle if the lengths of its two sides are given.

Figure Right Triangle Shorter Leg (a) Longer Leg (b) Hypotenuse (c)
A 3 5
c B 5 12
a
C 24 25
b
D 8 15
E 9 41

After the activity, the teacher will then discuss to the class the answers to the given
activity. Whoever got a perfect score will be rewarded.

G. Finding practical Given these situations, students will be introduced to the real-life application of Pythagorean
applications of concepts and Theorem.
skills in daily living 1. A 15-foot tree casts a shadow that is 8 feet long. What is the distance from the tip of
(ELABORATE) the tree to the tip of its shadow?
2. Joey made a sandwich that was 4 inches wide and 6 inches long. If he cuts the
sandwich in half as shown in the figure, what would be the diagonal length of the
sandwich?
3. Joshua won a laptop in a school raffle. The laptop screen measures 10 inches in
height and 24 inches in width. Find the diagonal length of the laptop screen.
4. The front view of a tent measures 6 feet across the bottom and 5 feet on the slant
sides. What is the height of the tent?
5. A baseball diamond is a square with sides of 90 feet. What is the shortest distance
from first base to third base?
H. Making generalizations The teacher will conduct an oral questioning to generalize and recall the concepts that have
and abstractions about the been discussed regarding Pythagorean Theorem.
lesson (ELABORATE)
I. Evaluating Learning Read and answer each of the following items accurately. Write the letter of the correct answer
(EVALUATE) on your answer sheet.
1. What do you call the longest side of a triangle?
a. Base b. Hypotenuse c. Leg d. Median

2. What triangle is formed if the lengths of the sides are 9 cm and 15 cm respectively?
a. Acute b. Equilateral c. Right d. Obtuse

3. Given at the right is ∆𝑁𝐸𝑊 with right  E. If w = 10

cm and n = 24 cm, find the value of e.
a. 26 cm b. 28 cm
c. 30 cm d. 40 cm

4. The length and width of a rectangle are 8 cm and 6 cm,

respectively. Find the length of the diagonal of the
rectangle.
a. 10 cm b. 15 cm
c. 20 cm d. 30 cm

5. If the foot of a 10-meter ladder is placed 6 meters from a

building, how high up the building will the ladder reach?
a. 8 m b. 16 m
c. 18 m d. 24 m

6. Dr. Young finds that his TV is 36 inches wide and 24 inches

tall. What is the length of the diagonal or the TV?
a. 27.43 inches b. 40.27 inches
c. 43.27 inches d. 50.27 inches

7. Fire fighters have a 40-foot extension ladder in order to

reach 28 feet up the building. How far away from the
building should the foot of the ladder be placed?
a. 28.57 ft. b. 30.57 ft.
c. 38.57 ft. d. 40.67 ft.

8. A flagpole stands 93 feet tall and is supported by a guy

wire measuring 157 feet long that is attached to the top
of the pole and to the ground some distance from the
base of the pole. Find the distance of the wire’s ground
attachment point from the base of the pole to the nearest
whole number.
a. 116 ft. b. 126 ft.
c. 136 ft. d. 156 ft.

9. The A-frame of the house is not drawn to scale. Find

the respective lengths of ̅̅̅̅
𝐺𝑂 and ̅̅̅̅
𝐺𝐷 .
a. 5.60 ft. and 8.40 ft.
b. 8.60 ft. and 6.40 ft
c. 10.60 ft. and 12.40ft.
d. 12.60 ft. and 16.40ft

10. Using Pythagorean Theorem, find an area of an equilateral triangle whose side
measures 7 inches to the nearest tenth of a square inch.
a. 21.2 sq. in. b. 21.3 sq. in. c. 42.4 sq. in. d.42.6 sq. in.

J. Additional activities for Students will be asked to consider the given situation and answer the questions that follow
application or remediation using their knowledge of the Pythagorean Theorem.
(EXTEND)
The heights of two buildings are 41 m and 32m and they are 12 m apart. A man went to the
rooftop of the shorter building and wondered looking at the rooftop of the taller building.
a. What could be the distance between the rooftops?
b. What could be the equation to use to represent the situation?
c. How much taller is one building than the other?
d. Try to do an experiment with a partner or group. Choose two buildings and find the
distance between their rooftops. Record the necessary measurements and write the
equation that represents the situation. Then determine the distance between the
rooftops.
V. REMARKS
VI. REFLECTION
A. No. of learners who earned 80%
on the formative assessment
B. No. of learners who require
additional activities for remediation
C. Did the remedial lesson work?
No. of learners who have caught
up with the lesson
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well? Why did these work?
F. What difficulties did I encounter
that my principal or supervisor can
help me solve?
G. What innovation or localized
materials did I use/ discover that I
wish to share with other teachers?

Prepared By:
Leosala, Ernie A.
Nuñez, Divine E.
Odeña, Mayca N.
Reptin, Odesa